Instability of magnetosonic waves in magnetized degenerate half-spin-polarized quantum plasma

Abstract

Shock and solitary waves in plasmas are the main focus of many current studies of localized disturbances in both laboratory and astrophysical plasmas. Here, the linear and the nonlinear properties evolving in three dimensions quantum magnetized spin-1/2 plasma formed of spin up (↑) and spin down (↓), nonrelativistic degenerate inertialess electrons, and classical ions, are considered. The nonlinear propagation is governed by a quantum Zakharov–Kuznetsov–Burger (QZKB) and QZK equations which are derived by using the multiple scales perturbation technique. The shock and solitary wave structures are dependent on the spin polarization parameter, Bohm potential, Zeeman energy, and dissipative parameter. The first, and the second, orders instability growth rates are also derived by using the small-k perturbation expansion method. The previous parameters affect also the instability growth rates. There is a critical angle below which the first order becomes positive while the second order is negative, and over which the first order disappears and the second order becomes positive. Our present results may be useful in understanding the dynamics in the magnetic pulsars, and also in the magnetic white dwarfs and neutron stars systems where degenerate spin-up and spin-down electrons with dissipative effects can exist.